Galileo’s Pendulum & Clock Jon Everett School of Physics UNSW

Vincenzo Galilei ( July 1591) Father of Galileo Musician/Composer Experimentalist

Galileo Galilei 15 February 1564 – 8 January 1642) 78 Physicist, Mathematician, Astronomer Philosopher, Musician Experimental Scientist Pendulum &Pendulum Clock

The Pendulum Re-discovered Up until Galileo’s discoveries the Pendulum was used primarily as a method of converting kinetic energy to Work

Cathedral Lamp Myth and Pendulum. It is claimed his interest had been sparked around 1582 by the swinging motion of a chandelier in the Pisa cathedral Pisa cathedral

Galileo discovered the crucial property that makes pendulums useful as timekeepers

Clocks before the Pendulum Various methods used for converting kinetic energy to move indicators to show time passed. All suffered from temperature, pressure and mechanical limitations. There was a need for an independant regulator.

De Dondi Padova ~1290

Praha Astro Clock 1410

De Dondi’s Astrium 1364

Palazzo Vecchio 1299

Galileo Moons of Jupiter & Longitude

Galileo the Clock Mechanic Galileo helped repair windows and personally took charge of keeping the convent clock in good repair.

History of Escapements Foliot (~1200) Verge (~1275) Pin Wheel Detent (Galileo ~ 1641) Anchor (Hooke ~ 1657) Deadbeat (Graham~1721) Grasshopper (Harrison~1722) Shortt (twin pendulum ~1922)

Galileo’s Escapement 1641

Huygens Model of Huygens pendulum clock, Huygens devised this model by attaching a pendulum to the gears of a mechanical clock. The regular swing of the pendulum allowed the clock to achieve greater accuracy. The hands are turned by the falling weight, which releases the same amount of energy with each tick. Galileo Galilei had already experimented with pendulums, but Huygens was the first to master and profit from it. In 1657, he was granted a patent and a few were made by Salomon Coster of The Hague.

This was a great improvement over existing mechanical clocks; their best accuracy was increased from around 15 minutes a day to around 15 seconds a day. [31] Pendulums spread over Europe as existing clocks were retrofitted with them. [31] retrofitted

Huygens ca 1670 with second hand dial

Huygens Pendulum Clock 1652

Physics of the Pendulum The Simple Pendulum If a pendulum of mass m attached to a string of length L is displaced by an angle Ɵ from the vertical.

it experiences a net restoring force due to gravity: F r = - mgsin Ɵ For small angles, sin Ɵ ≈ Ɵ, providing is expressed in radians (try it on your calculator for = 0.1,0.5,1.0 radians). In terms of radians Ɵ = S/L radians where s is the arc length and L is the length of the string. Thus, for small displacements, s, the restoring force can be written: F restoring = ma tangential mg sinθ = ma tangential For small oscillations the period of a simple pendulum is therefore given by

This 19th century model is based on a drawing by Galileo’s friend and biographer, Viviani, of an incomplete pendulum clock which Galilei Galileo ( ) designed just before his death. It represents the first certain known attempt to apply a pendulum to control the rate of a clock. The application of the pendulum to clock timekeeping during the 17th century scientific revolution was one of the most fundamental advances in the history of time measurement.

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